SAT Math Multiple Choice Question 268: Answer and Explanation
The figure above shows part of the path of a planned roller coaster hill. What is the sum, in feet, of the vertical height and the horizontal distance that the roller coaster will travel while on this particular hill?
- A. 220
- B. 300
- C. 460
- D. 900
Correct Answer: C
Category: Passport to Advanced Math / Scatterplots
Strategic Advice: Make sure you read the axis labels and the question carefully. You'll also need to rely on your knowledge of quadratic equations.
Getting to the Answer: The question asks for the sum of the vertical height and the horizontal distance that the roller coaster will travel above ground. The data points follow a parabolic (U-shaped) path, which means you can use properties of quadratic equations to find the solution. The vertical height is fairly straightforward-the vertex of the parabola is located at (110, 80), so the vertical height that the roller coaster reaches is 80 yards (notice the units). To find the horizontal distance, think about symmetry. Because the vertex occurs at a distance of 110 feet, the total horizontal distance that the roller coaster will travel is twice that, or 220 feet. Convert 80 yards to feet and add the result to 220 to arrive at the correct answer, 80 × 3 = 240 and 240 + 220 = 460 feet.